Deep tensor decomposition: A survey

Tensor decomposition (TD) has been recognized as an effective technique for multilinear dimensionality reduction and feature extraction for decades. However, traditional TD approaches often struggle to capture complex hierarchical structures and nonlinear relationships in high-dimensional datasets. For instance, in biomedical settings, disease groups may naturally contain subgroups or exhibit hierarchical structures; mechanistic interactions among diseases, drugs and targets often demonstrate nonlinearity. To address these challenges, a new paradigm, deep tensor decomposition (deep TD) has recently emerged inspired by the success of deep learning. Deep TD techniques can be mainly divided into two categories: linear and nonlinear deep TD. Linear deep TD exploits the layered structure of deep neural networks (DNNs) to recursively factorize factor matrices obtained from the classic TD enabling feature extraction at multiple levels of granularity. Nonlinear deep TD leverages the expressive power of DNNs to capture nonlinear correlations within the data. Despite rapid progress, there remains no unified treatment of deep TD methods. In this survey, we provide a comprehensive review of deep TD models, together with the deep learning training schemes for TD, and applications of deep TD models. Finally, we discuss open challenges and outline promising directions for future research.